The graph of F(x), shown below, resembles the graph of G(x)= x², but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x+4)2 +4
B. F(x)=3(x-4)2 - 4
C. F(x)=-3(x+4)² +4
D. F(x) = -3(x-4)² +4

Answer:

1st option

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 2, 1 ) and r = 3 , then

(x - (- 2) )² + (y - 1)² = 3² , that is

(x + 2)² + (y - 1)² = 9 ← expand factors using FOIL

x² + 4x + 4 + y² - 2y + 1 = 9

x² + 4x + y² - 2y + 5 = 9 ( subtract 9 from both sides )

x² + 4x + y² - 2y - 4 = 0 , that is

x² + y² + 4x - 2y - 4 = 0 ← in general form

Answer:

[tex]\textsf{1)} \quad x^2+y^2+4x-2y-4=0[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies (x-(-2)^2+(y-1)^2=3^2[/tex]

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

Expand and simplify:

[tex]\implies (x+2)^2+(y-1)^2=9[/tex]

[tex]\implies x^2+4x+4+y^2-2y+1=9[/tex]

[tex]\implies x^2+y^2+4x-2y+5=9[/tex]

[tex]\implies x^2+y^2+4x-2y-4=0[/tex]

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Answer:

Step-by-step explanation:

If AC is a supplementary line, then

x + 90° + x = 180°

solution:

2x + 90° = 180°   |subtract 90° from both sides

2x = 90°    |divide both sides by 2

x = 45°

Answer:

[tex] \sf \: b) \: {45}^{o} [/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + x + 90° = 180°

Then the value of x will be,

→ x + x + 90° = 180°

→ 2x = 180° - 90°

→ 2x = 90°

→ x = 90° ÷ 2

→ [ x = 45° ]

Hence, the value of x is 45°.

Answer: No it could not be ACB.

Step-by-step explanation:

Angles are named based on the vertex of the angle so this could be referred to as ∠B. The other way to name an angle is by saying the three points, However, when you say the three points the vertex must be in the middle. Hence, the answer is ∠CBA as the middle point of the angle is in the middle of the name.

Answer: 45

Step-by-step explanation: I used a graphing calculator and input all the equations and all the restraints, and I found that you can’t use the first equation since x has to be less than or equal to -3, and the question calls for x to be -2. So, in the second equation, there’s a point (-2, 16) and in the third equation there’s a point (1, -3). You know you have to use these two points since in the second equation, the restraint only lets you use numbers greater than -3 or less than 0, which cannot be one, and in the third equation, the restraint only lets you use numbers greater than 0, which can’t be -2. I hope that made some sense. So then, with substitution the equation would be 3(16)+(-3) which equals 45. 3(16)=48. 48-3+=45

Using limits, it is found that the end behavior of the graph is given as follows:

It rises to the left, and stays constant at y = -4 to the right.

It is given by the limits of f(x) as x goes to infinity.

In this problem, the function is given by:

[tex]f(x) = 4\left(\frac{2}{5}\right)^{x + 3} - 4[/tex]

Hence:

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{5}{2}\right)^{\infty + 3} - 4 = \infty - 4 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{2}{5}\right)^{\infty + 3} - 4 = 0 - 4 = -4[/tex]

Hence:

It rises to the left, and stays constant at y = -4 to the right.

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The direct proportion is shown by table (B)

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Here the second table shows the direct proportion relation.

This is because the ratio of x/y remain same.

4/2= 7/3.5= 10/5= 11/5.5= 15/7.5 = 2/1

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The simplified expression of [tex]x^{-2/3} . x^{6/7}[/tex] is [tex]x^{4/21}[/tex]

The expression [tex]x^{-2/3} . x^{6/7}[/tex] can be simplified as follows:

using law of indices,

xⁿ . xᵇ = xⁿ⁺ᵇ

Therefore,

[tex]x^{-2/3} . x^{6/7}[/tex] = [tex]x^{-2/3 + 6/7}[/tex]

[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21}[/tex]

[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21} = x^{4/21}[/tex]

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Answer:

Step-by-step explanation:

Is there answer choices?

Answer:

700 kWh which is more than 200 so

0.10(x - 200) + 30

0.10( 700 -200)+ 30

0.10( 500) + 30

50 + 30

80

$80

Answer:

(-4,-2)

x=-4

y=-2

Step-by-step explanation:

-3x-4y=20

3(x-10y=16)=3x-30y=48

The reason I multiplied 3 to the second equation is for when we add the equations together the x will cancel out.

  -3x-4y=20

+  3x-30y=48

  -34y=68

Divide -34 from both sides.

y=-2

To find x you need to plug in -2 for y into one of the equations.

x-10y=16

x-10(-2)=16

Remember a negative times a negative equals a positive.

x+20=16

Subtract 20 from both sides.

x=-4

Hope this helps!

If not, I am sorry.

Answer:

1•4

Step-by-step explanation:

1•54÷1•1

1•54

1•1

divide by 10 both side with can move decimal

15•4

11

=my answer is 1•4.

Answer:

The correct answer for algebraic expression 1.54÷1.1 is = 1.4.

Step-by-step explanation:

this is question based on simple algebra -

Simple Algebraic equations -  An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.

these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials

so in the question algebraic operation used to solve is simple division.

therefore here in question we have to divide 1.54 with 1.1,

using the concept written above,

let the value of division be 'x'

we can write 1.54/1.1 = x

by dividing and multiplying the equation by 100 to remove the decimals.

            (1•54/ 1•1)×100/100    = x

                    154/110    =  x

now by simple division,

                      1.4   =  x  answer

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Answer:

g(x) = (x - 5)²

Step-by-step explanation:

This is an example of the transformation of functions.

In this example, we see the graph f(x) has been moved 5 in the positive direction on the x-axis.

Due to the fact that we are working with the x-axis, our transformation will be placed inside the bracket, and it will do the opposite of what we expect.

This means that our transformation will be set out in this format:

[tex]g(x) = f(x-5)[/tex]

We know that:

[tex]f(x) = x^2[/tex]

Therefore,

[tex]g(x) = f(x-5) = (x-5)^2[/tex]

So, [tex]g(x) = (x-5)^2[/tex].

Answer:

7/9     ( or  7:9)

Step-by-step explanation:

Children = 35

Total people = 35 + 10 = 45

ratio Children / total people =  35/45  = 7/9

Answer:

2x(x^2 - 3)(x^2 + 9)

Step-by-step explanation:

2x^5 + 12x^3 − 54x

2x(x^4 + 6x - 27)

Since -3 + 9 = 6 and -3 x 9 = -27:

2x(x^2 - 3)(x^2 + 9)

Answer:

[tex]2x(x^2-3)(x^2+9)[/tex]

Step-by-step explanation:

Given polynomial:

[tex]2x^5+12x^3-54x[/tex]

Factor out the common term [tex]2x[/tex]:

[tex]\implies 2x(x^4+6x^2-27)[/tex]

To factor the trinomial [tex]x^4+6x^2-27[/tex]:

[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]

Factor the quadratic by finding two numbers that multiply to -27 and sum to 6:  9 and -3

Rewrite the middle term as the sum of these two numbers:

[tex]\implies u^2+9u-3u-27[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies u(u+9)-3(u+9)[/tex]

Factor out the common term (u + 9):

[tex]\implies (u-3)(u+9)[/tex]

Substitute back [tex]u=x^2[/tex]:

[tex]\implies (x^2-3)(x^2+9)[/tex]

Therefore, the factored form of the given polynomial is:

[tex]\implies 2x(x^2-3)(x^2+9)[/tex]

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function [tex]y(t)=e^t[/tex]  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

[tex]y_1(t) = e^t[/tex]

Given differential equations are,

y''-y = 0

 So that,  

[tex]y' (t) = e^t, y'' (t) = e^t[/tex]

Substitute values in the given differential equation.

[tex]e^t -e^t=0[/tex]

Therefore, the function [tex]y(t)=e^t[/tex]  is the solution of the given differential equation.

Another function;

[tex]y(t)=cosht[/tex]  

So that,  

[tex]y"(t)=sinht\\\\y"(t)=cosht[/tex]

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:it is o to 10/5 which is 1/

Step-by-step explanation:

Answer:

pete

Step-by-step explanation:

i think its pete???

Answer:

The answer is 1: 50000... If you look down here↓:

Step-by-step explanation:

With a scale of 1:20000, a unit length on the map represents a length of 20000. So 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 will be = 4*10^8 cm^2.

50 cm^2 represents that 4*50*10^8 cm^2 = 200* 10^8 cm^2.

Now, on the other hand, the map has the same. 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.

Therefore the scale on the second map is 1: 50000.

Answer:

D.All of the choice

Step-by-step explanation:

D.All of the choice

Answer:

48

Step-by-step explanation:

The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: [tex]mean = \frac{sum}{amountnumbers}[/tex].

When we plug our values into this equation, we get: [tex]6 = \frac{sum}{8}[/tex]. Solving this equation gets us sum = 6 * 8 = 48

In order to evaluate consistency in studies with more than one data collector, the Inter-rater reliability is used.

This is a measure in research that is used to test the data presented by different data collectors, for consistency.

It essentially checks the extent to which the data collected from the different sources agree with each other.

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Using the cosine ratio, the expression that can be used to determine the  side length of the given rhombus is: x = 10/cos 30.

The cosine ratio that can be used to solve a right triangle is, cos ∅ = adj/hyp.

x represents the side of the rhombus as shown in the image attached.

cos 30 = 10/x

x(cos 30) = 10

x = 10/cos 30

Thus, the equation that would be used to determine the side length is: x = 10/cos 30

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Answer:

A

Step-by-step explanation:

10/cos 30°

Answer:

B

Step-by-step explanation:

Similar to the one you asked earlier.

Given from the table

1 Gallon of gas = $2.15

15 gallons of gas = $2.15 x 15

= $32.25 (B)

The x-coordinate of the point (50, 55) is 50

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The distance of point (50, 55) perpendicular to y-axis

Thus, perpendicular distance = 50 units

The x-coordinate of the point (50, 55) is 50

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The correct answer is option b which is the exponential grows at the same rate as the quadratic.

The complete question is given below with the graph attached:-

An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval

a. The exponential grows at half the rate of the quadratic.

b.The exponential grows at the same rate as the quadratic.

c.The exponential grows at twice the rate of the quadratic.

d.The exponential grows at four times the rate of the quadratic.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval

a ≤ x ≤ b

is given by

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval

0 ≤ x ≤ 1

is given by

[tex]\dfrac{f(1)-f(0)}{1-0}= \dfrac{2-1}{1}=1[/tex]

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval

0 ≤ x ≤ 1

is given by

[tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{1-0}{1}=1[/tex]

Therefore, the exponential grows at the same rate as the quadratic in the interval .

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Answer:

-23

Step-by-step explanation:

f(2)= 2*2-6 = -2

g(-3)= -3-2*9 = -21

---> f(2)+G(-3)= -2-21 = -23

Answer: -23

Step-by-step explanation:

     f(2) + g(-3) means that we will substitute 2 as x into the function f, and add that to -3 substituted as x into function g.

     First, we will find the substituted and simplified values of these functions.

f(x) = 2x - 6

f(2) = 2(2) - 6

f(2) = -2

[tex]-----[/tex]

g(x) = x - 2x²

g(-3) = (-3) - 2(-3)²

g(-3) = -21

     Lastly, we can add them.

f(2) + g(-3)

-2 + -21

-23

Answer:

6 square units

Step-by-step explanation:

base = 4 units

height = 3 units

 [tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*base*height}[/tex]

                                  [tex]\sf =\dfrac{1}{2}*4*3\\\\ = 2*3\\\\ = 6 \ square units[/tex]

[tex]\Large❏ \: \large\begin{gathered} {\underline{\boxed{ \rm {\blue{Area \: of \: triangle \: = \: \frac{1}{2} \: \times \: Base \: × \: Height }}}}}\end{gathered}[/tex]

[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{2} \: \times \: Base \: × \: Height [/tex]

[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{2} \: \times \: 4 \: × \: 3 [/tex]

[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: \frac{1}{ \cancel2} \: \times \: \cancel{4} \: ^{\green2} \: × \: 3 [/tex]

[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: 2 \: \times \: 3[/tex]

[tex]\rm \large \red{\: Area \: of \: triangle }\large\purple\implies \tt \large \: 6[/tex]

Hence , the area of triangle is 6 units.

The composite function (boa)(x) is equivalent to √3x-3

Given the following functions

a(x) = 3x +1

b(x) = √x - 4

To determine the composite function (boa)(x)

b(a(x) = b(3x +1)

Substitute 3x + 1 into b(x) to have:

(boa)(x)= √(3x + 1) - 4

(boa)(x) = √3x-3

Hence the composite function (boa)(x) is equivalent to √3x-3

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Step-by-step explanation:

We can solve this kind of trigonometric problem

easily by the followings method :

Given :

cos^4a + cos^2a = 1

or, cos4^a = 1 - cos^2a

Therefore; cos^4a = sin^2a

Again,

To prove: cot^4a - cot^2a = 1

L.H.S = Cot^4a - cot^2a

= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a

= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a

= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a

= 1 - cos^2a ÷ Sin^2a

= Sin^2a ÷ Sin^2a

= 1 = R.H.S proved.

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We use Tan in this case:

Tan=(opposite/adjacent)

Tan(36)=23/x

x=23/Tan(36)

x=31.64 length

Hope it helps!

Answer:

x ≈ 31.64

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

The given trigonometric ratios all use the angle of 36°.

From inspection of the given diagram:

Therefore, we should use the tan trig ratio.

[tex]\implies \sf \tan(36^{\circ})=\dfrac{23}{x}[/tex]

[tex]\implies \sf x=\dfrac{23}{\tan(36^{\circ})}[/tex]

Substituting the given value for tan 36°:

[tex]\implies \sf x \approx \dfrac{23}{0.727}[/tex]

[tex]\implies \sf x\approx31.64[/tex]